The highly-rated 21-year-old could be available for a mere £3m with the Porto winger entering the final year of his contract.
Porto have failed on a number of occasions to extend the winger's contract with Atsu able to agree a Bosman deal with other clubs in January.
Mourinho is believed to be keen to add the Ghanian to his growing midfield contingent before the transfer window shuts next week.
Atsu will join Willian who joined the Europa League champions earlier this week in a deal reportedly around £30m.
Willian looked certain to join Spurs after completing his medical but a late intervention from Chelsea saw the Brazilian head towards Stamford Bridge.
Former Anzhi Makhachkala team mate Samuel Eto'o is also expected to join the Blues in the next 48 hours as Mourinho looks to find a frontman after seemingly missing out on main target Wayne Rooney.
Elsewhere Demba Ba's short Chelsea stint looks to have come to a temporary end, after Newcastle entered talks to try and re-capture their man on loan.
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